The GNSS integer ambiguities: estimation and validation

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Bibliography Abidin HA (1993). Computational and geometrical aspects of on-the-fly ambiguity resolution. Ph.D. Thesis, Dept. of Surveying Engineering, Techn.Report no.104, University of New Brunswick, Canada, 314 pp. Baarda W (1968). A testing procedure for use in geodetic networks. Publications on Geodesy, 2(5), Netherlands Geodetic Commission, Delft. Baarda W (1973). S-transformations and criterion matrices. Publications on Geodesy, 5(1), Netherlands Geodetic Commission, Delft. Betti B, Crespi M, Sansò F (1993). A geometric illustration of ambiguity resolution in GPS theory and a bayesian approach. Manuscripta Geodaetica, 18: 317–330. Blewitt G (1989). Carrier-phase ambiguity reolution for the Global Positioning System applied to baselines up to 2000 km. Journal of Geophysical Research, 94(B8): 10187– 10302. Bona P (2000). Precision, cross corelation, and time correlation of GPS phase and code observations. GPS Solutions, 4(2): 3–13. Bona P, Tiberius CCJM (2001). An experimental assessment of observation crosscorrelation in dual frequency GPS receivers. Proc. of ION GPS-2000, Salt Lake City UT : 792–798. Borre K, Tiberius CCJM (2000). Time series analysis of GPS observables. Proc. of ION GPS-2000, Salt Lake City UT : 1885–1894. Brent R (1973). Algorithms for minimization without derivatives. Prentice-Hall. Chen D, Lachapelle G (1995). A comparison of the FASF and least-squares search algorithms for on-the-fly ambiguity resolution. Navigation, 42(2): 371–390. Chen Y (1997). An approach to validate the resolved ambiguities in GPS rapid positioning. Proc. of the International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, Banff, Canada. De Jonge PJ, Tiberius CCJM (1996). The LAMBDA method for integer ambiguity estimation: implementation aspects. Delft Geodetic Computing Centre, LGR series No.12, Delft University of Technology, 49pp. Dong D, Bock Y (1989). Global Positioning System network analysis with phase ambiguity resolution applied to crustal deformation studies in California. Journal of Geophysical Research, 94(B4): 3949–3966. Erhard P (2002). Status of Galileo navigation signals, Design and frequency plan. ESA publication ”ESA-APPNG-TN/00407/PhE”, 59 p. 163
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The GNSS integer ambiguities: estim
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The GNSS integer ambiguities: estim
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Contents Preface v Summary vii Same
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4 Best Integer Equivariant estimati
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Preface It was in the beginning of
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• No attempt is made to fix the a
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Samenvatting (in Dutch) De GNSS geh
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gelegd door de keuze van de maximaa
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d, δ instrumental delay for code a
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Acronyms ADOP Ambiguity Dilution Of
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in practice, a user has to choose b
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GNSS observation model and quality
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Table 2.2: Signal and frequency pla
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2.2.2 Phase observations The phase
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the propagation delay does not depe
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2.2.9 The geometry-based observatio
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2.3.2 Single difference models If o
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and difficult to predict. Therefore
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The double difference observation v
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(appendix A.1): Qy = C sd pφ ⊗ D
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The quality of the solution can the
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is maximum. The degrees of freedom
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* â Figure 3.1: An ambiguity pull-
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2 1.5 1 0.5 0 −0.5 −1 −1.5
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estimator is given by: n Sz,B = x
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7 6 5 4 3 2 1 0 −1 −2 −3 −4
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Table 3.1: Overview of ambiguity re
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1 0.5 0 −2 −1 0 1 z 2 1 0 −1
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and has units of cycles. It was int
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chosen equal to half the number of
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Table 3.2: Two-dimensional example.
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The bias-affected success rate is a
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is close to one. This probability c
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2 0 −2 0.5 0 −0.5 2 0 −2 −4
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error in pdf error in pdf error in
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0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2 2.2
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acceptable. Moreover, the bounds wi
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Unfortunately, this relatively simp
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always larger than one. This shows
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where χ2 α(m−p, 0) is the criti
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Table 3.5: Overview of all test sta
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with the weight function wz(â) = 1
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IE IEU IU LU Figure 4.1: The set of
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4.2 Approximation of the BIE estima
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4.3 Comparison of the float, fixed,
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variane ratio 1.4 1.2 1 0.8 0.6 0.4
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ambiguity residual 0.5 0.4 0.3 0.2
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Table 4.1: Probabilities P1 = P (|
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Table 4.2: Probabilities Ps = P (ǎ
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Table 4.4: Probabilities that float
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probability probability 1 0.9 0.8 0
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Integer Aperture estimation 5 In se
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can be distinguished: â ∈ Ωa s
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and the hybrid distribution of ā i
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Figure 5.3: 2-D example for EIA est
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as follows: Ωz,R = ΩR ∩ Sz =
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3 2.5 2 1.5 1 0.5 0 −0.5 −1 −
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5.3.3 Difference test is an IA esti
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Figure 5.9: 2-D example for DTIA es
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Figure 5.11: 2-D example for PTIA e
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Figure 5.12: 2-D example for IAB es
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2-D example Figure 5.13 shows in bl
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µ 200 100 10 2 1 1 1.1 1.2 1.3 1.4
Page 137 and 138: 5.6 Optimal Integer Aperture estima
Page 139 and 140: The optimization problem of (5.49)
Page 141 and 142: Table 5.1: Comparison of IA estimat
Page 143 and 144: µ 1.5 1.45 1.4 1.35 1.3 1.25 1.2 1
Page 145 and 146: In order to show that the fail rate
Page 147 and 148: success rate percentage identical 0
Page 149 and 150: probability probability 1 0.9 0.8 0
Page 151 and 152: 5.8.2 OIA estimation versus RTIA an
Page 153 and 154: µ µ µ 0.7 0.6 0.5 0.4 0.3 0.2 0.
Page 155 and 156: 0.6 0.4 0.2 0 −0.2 −0.4 −0.6
Page 157 and 158: three vc-matrices which are scaled
Page 159 and 160: Table 5.3: Comparison of IAB and IA
Page 161 and 162: success rate if fixed 1 0.95 0.9 0.
Page 163: Table 5.4: Overview of IA estimator
Page 166 and 167: IE IA I Figure 6.1: The set of rela
Page 168 and 169: convex region symmetric with respec
Page 171 and 172: Mathematics and statistics A A.1 Kr
Page 173 and 174: The expectation, E{x}, and the disp
Page 175 and 176: Choose the tolerance ε. Determine
Page 177 and 178: Simulation and examples B Throughou
Page 179 and 180: Theory of BIE estimation C In chapt
Page 181 and 182: The first term on the right-hand si
Page 183: can be derived: L = {2h(x) T Q
Page 186 and 187: 1. Choose fixed fail rate: Pf = β
Page 190 and 191: Euler HJ, Goad C (1991). On optimal
Page 192 and 193: Teunissen PJG (1995). The least-squ
Page 194 and 195: Verhagen S, Teunissen PJG (2004c).
Page 196: probability density function, 37 pr
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